# Power Laws and Luxury Goods

As Chris Anderson knows,

once you start thinking in terms of power laws you start seeing them everywhere.

But it’s worth drawing a distinction between power laws as a meme and power

laws as something mathematically well-defined.

After posting a piece

on power laws in the housing market, I got an email from one of my more devoted

readers (OK, my father) asking if I had the vaguest notion what I was talking

I would like to know if there is any statistical basis for the alleged "power

law distribution" of house prices in different cities or whether it is

just journalese (as in "exponential" which is one of the most misused

words around).

Good question. And the answer is, frankly, "just journalese". Specifically,

I would never try to discern the distinction between a power-law distribution

and a lognormal distribution – when I use the term "power law",

I basically mean "something with a much longer and fatter tail than your

standard Gaussian bell-curve distribution".

Let’s get away from housing and think about luxury goods. And let’s look at

the tail — specifically, at the top 1% of the market. (Either the market in

general, or any market in particular, such as wristwatches,

for example.) Now look at the top 1% of that top 1%.

If your distribution is Gaussian, there isn’t an enormous amount of difference

between the top 0.01% and the top 1%. It’s there, but the top 0.01% won’t be

more than two or three times as expensive as the top 1% generally. But if you

have a power-law distribution going on, then the top 0.01% will be vastly more

expensive, maybe 100 times more expensive, than the top 1% generally. If you

have a lognormal distribution, then you’ll be somewhere in between.

The power-law thesis is that many parts of the world are moving away from normal

distributions and towards distributions which look much more like lognormal

or power-law distributions. Check out Merrill Lynch, which has just launched

a luxury-goods "LifeStyle

Index", a "tradable certificate" which tracks the earnings

of the luxury-goods sector.

The performance of the index has been back-tested from January 2000 against

the major broad benchmarks for the global consumer discretionary sector, namely

the MSCI World Consumer Discretionary index. The average outperformance of

the index versus its benchmark currently stands at almost 8 percent despite

a similar volatility and a dividend yield that is 20 percent higher on average.

This performance illustrates the theoretical efficacy of the index together

with the inherent value of brand names associated with luxury goods and lifestyle

stocks.

In other words, this index is a bet that the rich will continue to get richer,

and that as and when they do so, they’re likely to splurge on ostentatious

displays of wealth from established brand-names.

Not a stupid bet to make, although of course if the stock market is already

pricing in those future earnings gains, Merrill’s index isn’t going to continue

to outperform.

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